/*=========================================================================

  Program:   Diffusion Applications
  Module:    $HeadURL$
  Language:  C++
  Date:      $Date$
  Version:   $Revision$

  Copyright (c) Brigham and Women's Hospital (BWH) All Rights Reserved.

  See License.txt or http://www.slicer.org/copyright/copyright.txt for details.

==========================================================================*/
#ifndef itkDiffusionTensor3DFSAffineTransform_txx
#define itkDiffusionTensor3DFSAffineTransform_txx

#include "itkDiffusionTensor3DFSAffineTransform.h"

namespace itk
{

template <class TData>
typename DiffusionTensor3DFSAffineTransform<TData>::MatrixTransformType DiffusionTensor3DFSAffineTransform<TData>::ComputeMatrixSquareRoot(MatrixTransformType matrix)
{
  MatrixTransformType sqrMatrix;

  vnl_matrix_fixed<double, 3, 3> M(3, 3);
  M = matrix.GetVnlMatrix();
  vnl_real_eigensystem eig(M.as_matrix());
  vnl_matrix_fixed<std::complex<double>, 3, 3> D(3, 3);
  vnl_matrix_fixed<std::complex<double>, 3, 3> vnl_sqrMatrix(3, 3);
  D.fill(NumericTraits<TData>::ZeroValue());
  for (int i = 0; i < 3; i++)
  {
    D.put(i, i, std::pow(eig.D.get(i, i), 0.5));
  }
  vnl_sqrMatrix = eig.V * D * vnl_matrix_inverse<std::complex<double>>(eig.V).as_matrix();
  vnl_matrix_fixed<double, 3, 3> vnl_sqrMatrix_real(3, 3);
  vnl_sqrMatrix_real = vnl_real(vnl_sqrMatrix);
  for (int i = 0; i < 3; i++)
  {
    for (int j = 0; j < 3; j++)
    {
      sqrMatrix[i][j] = vnl_sqrMatrix_real.get(i, j);
    }
  }
  return sqrMatrix;
}

template <class TData>
void DiffusionTensor3DFSAffineTransform<TData>::PreCompute()
{
  InternalMatrixTransformType m_RotationMatrix;

  m_RotationMatrix = ComputeRotationMatrixFromTransformationMatrix();
  InternalMatrixTransformType MeasurementFrameTranspose = this->m_MeasurementFrame.GetTranspose();
  InternalMatrixTransformType RotationMatrixTranspose = m_RotationMatrix.GetTranspose();
  // Instead of computing the inverse transform (which go from the input image to the output image)
  // and compute the rotation matrix from the inverse, we compute the rotation matrix from the original
  // transform and takes its inverse (=transpose since it is a rotation). Both rotation matrices are equals,
  // therefore we avoid computing the inverse of our original transform since it is not necessary.
  this->m_TransformT = MeasurementFrameTranspose * m_RotationMatrix;
  this->m_Transform = RotationMatrixTranspose * this->m_MeasurementFrame;

  this->ComputeOffset();
  this->m_LatestTime = Object::GetMTime();
}

template <class TData>
typename DiffusionTensor3DFSAffineTransform<TData>::MatrixTransformType DiffusionTensor3DFSAffineTransform<TData>::ComputeRotationMatrixFromTransformationMatrix()
{
  MatrixTransformType m_RotationMatrix;
  InternalMatrixTransformType TransformMatrixTranspose = this->m_TransformMatrix.GetTranspose();
  MatrixTransformType matrix;

  try
  {
    matrix = ComputeMatrixSquareRoot(this->m_TransformMatrix * TransformMatrixTranspose).GetInverse();
  }
  catch (...)
  {
    itkExceptionMacro(<< "Matrix is not invertible while computing rotation matrix");
  }
  m_RotationMatrix = matrix * static_cast<MatrixTransformType>(this->m_TransformMatrix);
  return m_RotationMatrix;
}

} // end namespace itk
#endif
